Two ice skaters, one with a mass of $57 \mathrm{~kg}$ and the other with a mass of $75 \mathrm{~kg}$, stand facing each other on the surface of a frozen pond. One of the skaters exerts a $135 \mathrm{~N}$ force against the other. Calculate the magnitude of the acceleration of each skater.

Two ice skaters are holding hands at the center of a frozen pond when an argument ensues. Skater A shoves skater $\mathrm{B}$ along a horizontal direction. Identify (a) the horizontal forces acting on $\mathrm{A}$

Two ice skaters are holding hands at the center of a frozen pond when an argument ensues. Skater A shoves skater $\mathrm{B}$ along a horizontal direction. Identify (b) those acting on $\mathrm{B}$.

A 2.7 kg block of wood sits on a frictionless table. A 3.0 g bullet, fired horizontally at a speed of 500 m/s, goes completely through the block, emerging at a speed of 220 m/s. What is the speed of the block immediately after the bullet exits?

A $60 \mathrm{~g}$ tennis ball with an initial speed of $32 \mathrm{~m} / \mathrm{s}$ hits a wall and rebounds with the same speed. Figure mentioned. shows the force of the wall on the ball during the collision. What is the value of $F_{\max }$, the maximum value of the contact force during the collision?

A solid cylinder with a radius of 4.0 cm has the same mass as a solid sphere of radius R. If the cylinder and sphere have the same moment of inertia about their centers, what is the sphere's radius?

A roller coaster car has a mass of $400 \mathrm{~kg}$ and a speed of $15 \mathrm{~m} / \mathrm{s}$.

a) What is the $K E$ of the roller-coaster cart?

b) What will be the GPE of this roller-coaster cart at its highest point, where $K E=0$ at that point?

c) How high can the roller-coaster cart go with this much energy?

500 J of work are done on a system in a process that decreases the system's thermal energy by 200 J. How much energy is transferred to or from the system as heat?

500 J of work are done on a system in a process that decreases the system’s thermal energy by 200 J. How much heat energy is transferred to or from the system?

A $60 \mathrm{~g}$ tennis ball with an initial speed of $32 \mathrm{~m} / \mathrm{s}$ hits a wall and rebounds with the same speed. FIGURE EX9.11 shows the force of the wall on the ball during the collision. What is the value of $F_{\max }$, the maximum value of the contact force during the collision?

A roller coaster car with mass $640 \mathrm{~kg}$ moves along the track shown in Figure 8. Assume all friction is negligible. (a) Is the mechanical energy of the roller coaster conserved? Explain your answer. (b) If the roller coaster starts from rest at point $\mathrm{A}$, what is its total mechanical energy at point $A$ ? (c) What is the total mechanical energy at point $\mathrm{B}$ ? (d) Calculate the speed of the roller coaster when it reaches points $\mathrm{B}$ and $\mathrm{C}$. (e) If the car starts with a speed of $12 \mathrm{~m} / \mathrm{s}$ at point $\mathrm{A}$, calculate the speed of the roller coaster when it reaches points $\mathrm{B}$ and $\mathrm{C}$.

Use the impulse-momentum theorem to find how long a stone falling straight down takes to increase its speed from 5.5 m/s to 10.4 m/s.

A 1000 kg sports car accelerates from 0 to 30 m/s in 10 s. What is the average power of the engine?

A sled and rider, gliding over horizontal, frictionless ice at 4.0 m/s, have a combined mass of 80 kg. The sled then slides over a rough spot in the ice, slowing down to 3.0 m/s. What impulse was delivered to the sled by the friction force from the rough spot?